[Urgent] I have a polynomial, and I need to find a and b but don't know how! (1 Viewer)

[GrizzlyPwnage]

This is the question and I dont know how to do it, any feedback would be appreciated.

When the polynomial 2x³+ax²+bx+1 is divided by x-1 the remainder is 4; when divided by x-2, the remainder is 21. Find the values of a and b.


[Edit]
I also have a second question which is similar, but I am still having trouble with.

Given that (x+1) and (x-2) are two factors of x⁴-3x³+ax²+bx+6, find a and b and the two other factors.

 

[seventhroot]

Re: [UrgentI have a polynomial, and I need to find a and b but don't know how!

sub in x = 1 and get an equation in a and b and equate that to 4

sub in x = 2 and get another equation in a and b and equate that to 21

solve equations simultaneously

 

[GrizzlyPwnage]

Re: [UrgentI have a polynomial, and I need to find a and b but don't know how!

Thankyou so much, I have my prelim exam on Tuesday and this really helps.

 

[GrizzlyPwnage]

Re: [UrgentI have a polynomial, and I need to find a and b but don't know how!

When you say "equate that to 4" what do you mean by that?

 

[seventhroot]

Re: [UrgentI have a polynomial, and I need to find a and b but don't know how!

sub everything in and then = 4

 

[GrizzlyPwnage]

Re: [UrgentI have a polynomial, and I need to find a and b but don't know how!

Okay thankyou, your help is much appreciated.

 

[seventhroot]

Re: [UrgentI have a polynomial, and I need to find a and b but don't know how!

nws

 

[GrizzlyPwnage]

If anyone would be able to help me with my second question It would be appreciated, thankyou.

 

[seventhroot]

If anyone would be able to help me with my second question It would be appreciated, thankyou.

it's the same thing as the first one and then divide use polynomial division to find the other factors

IMO; you really need to work on your problem solving skills. you need to be able to read the question -> abstract it -> solve the problem

 

[braintic]

then divide use polynomial division to find the other factors

Or use sum and product of roots to find the quadratic which has the other zeros as roots

 

[seventhroot]

Or use sum and product of roots to find the quadratic which has the other zeros as roots

ohh yeah this would be a better way because you have already obtained the roots from the 1st part

repped

 

[Carrotsticks]

You can find the two other factors without finding A and B.

 

[GrizzlyPwnage]

Back again today, Im having trouble with my polynomials in general so sorry for all the questions.

The polynomial f(x)= ax²+bx+c has zeros 4 and 5, and f(-1) = 60. Evaluate a,b and c.

 

[seventhroot]

what have you attempted thus far? there is no point me typing all the answers and you doing nothing

 

[Drongoski]

Back again today, Im having trouble with my polynomials in general so sorry for all the questions.

The polynomial f(x)= ax²+bx+c has zeros 4 and 5, and f(-1) = 60. Evaluate a,b and c.

This is only a quadratic. Fact it has zeros 4 and 5 means:

f(x) = a(x-4)(x-5)

f(-1) = a(-1-4)(-1-5) = 60 ==> 30a = 60 ==> a = 2

So f(x) = 2(x-4)(x-5) = 2x^2 - 18x + 40

So: a=2, b=-18 and c=40

 

[seventhroot]

This is only a quadratic. Fact it has zeros 4 and 5 means:

f(x) = a(x-4)(x-5)

f(-1) = a(-1-4)(-1-5) = 60 ==> 30a = 60 ==> a = 2

So f(x) = 2(x-4)(x-5) = 2x^2 - 18x + 40

So: a=2, b=-18 and c=40

this is a nice solution. Personally I didn't see that and would have set up a Matrix

 

[photastic]

Re: [UrgentI have a polynomial, and I need to find a and b but don't know how!

Thankyou so much, I have my prelim exam on Tuesday and this really helps.

Lol